General Assembly, considered the best horse of his generation last summer but virtually ignored here this week, gave a dramatic indication this morning that he could be a serious contender in the Kentucky Derby.

The son of Secretariat worked five furlongs at Churchill Downs in a blistering 57 2/5 seconds. No Derby contender has worked as fast since Forego went the same distance in 57 seconds in 1973.

Under jockey Bill Gavidia, General Assembly sped his final eighth of a mile in a sensational 11 3/5 seconds, and then galloped out six furlongs in 1:10 1/5. The move was considerably more impressive than those by Derby favorites Spectacular Bid and Flying Paster earlier in the week.

Trainer LeRoy Jolley was delighted by his colt's effort. "General Assembly seemed to like the track," he said. "He seems to run best after he works best, somewhat like Secretariat and Foolish Plasure (whom Jolley trained to win the 1975 Derby). I think we have a chance on Saturday."

Ordinarily, a workout during the last two days before the Derby doesn't shed much new light on a horse's capabilities or condition. But General Assembly has been such an enigma throughout much of his career that nobody knows what to expect of him from one week to the next.

The colt was the talk of the New York racing world even before he competed, partly because of reports of his precocity but mostly because of his striking resemblence to his father. General Assembly lived up to his advance billing by winning the first three races of his career, but his reputation was tarnished when he met Spectacular Bid and was soundly beaten twice.

This season, General Assembly's performances have been almost unfathomable. He lost his first two starts of the season, running very poorly, and then captured the Gotham Stakes at Aqueduct with an excellent effort. That victory semed to suggest that General Assembly has recaptured his 2-year-old form, but he followed it by a mediocre fifth-place finish in the Wood Memorial Stakes.

His detractors say that General Assembly has not heart, no true competitive spirit. But erratic behavior in thoroughbreds is more often the result of physical problems than mental ones, and General Assembly has been botherea by a troublesome right ankle throughout much of his career.

Horses with ankle or knee problems usually cannot sustain consistent performances. Their trainers can only crank them up for periodic big efforts. This might explain General Assembly's in-and-out efforts, and also Jolley's willingness to dismiss the Wood result and come here for the Derby.

If General Assembly is indeed the kind of horse who can only produce intermittent big efforts, Jolley will surely try to have him produce one Saturday. Today's workout confirms that notion. CAPTION: Picture, Trainer LeRoy Jolley restrains General Assembly while groom unwraps bandages after a sizzling workout for Derby. AP